Finite Group Databasebeta

← C3×#10599136 #14284032

Subgroups — C3×#10599136 #14284032

Order 1920.

528 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D5×#124C211yesmaximal, characteristic
2C3×#64996C211yesmaximal, characteristic, complemented
3C3×#64994C211yesmaximal, characteristic, complemented
4C3×C5×#329C211yesmaximal, characteristic, complemented
5C3×#64760C211yesmaximal, characteristic, complemented
6C3×#64684C211yesmaximal, characteristic, complemented
7C3×#64684C211yesmaximal, characteristic, complemented
8#10599136C311yesmaximal, characteristic, direct product factor, Hall
9C2×C3×Q8×D5C411yescharacteristic
10C2×C3×D4×D5C411yescharacteristic
11C3×C5×#124C2211yescharacteristic
12C3×#4093C411yescharacteristic
13C3×#4082C411yescharacteristic
14C2×C3×#676—21no—
15C3×#4031—21no—
16C3×#4031—21no—
17C3×D5×C22⋊C4—21no—
18C3×D5×C22⋊C4—21no—
19C3×#4021C2211yescharacteristic
20C3×C42×D5C2211yescharacteristic
21C3×C5×#97C2211yescharacteristic, complemented
22C3×C5×#97C2211yescharacteristic, complemented
23C3×#3952—21no—
24C3×#3946—21no—
25C3×C8×Dic5—21no—
26C3×#3935C2211yescharacteristic, complemented
27C3×#3935C2211yescharacteristic, complemented
28C3×#1527—51nomaximal, Hall
29D5×#124C2×C311yescharacteristic
30#64996C2×C311yescharacteristic, complemented
31#64994C2×C311yescharacteristic, complemented
32C5×#329C2×C311yescharacteristic, complemented
33#64760C2×C311yescharacteristic, complemented
34#64684C2×C311yescharacteristic, complemented
35#64684C2×C311yescharacteristic, complemented
36C23×C3×D5—21no—
37C2×C3×C5×Q8C2×C411yescharacteristic
38C2×C3×C5×D4C2×C411yescharacteristic
39C2×C3×C22⋊D5—21no—
40C3×Q8×D5—42no—
41C3×D4×D5—42no—
42C2×C3×D20C2×C411yescharacteristic
43C2×C3×C4×D5—21no—
44C2×C3×C4×D5C2×C411yescharacteristic
45C2×C3×C4×D5D411yescharacteristic
46C2×C3×C4×D5D411yescharacteristic
47C2×C3×Dic10—21no—
48C2×C3×Dic10C2×C411yescharacteristic
49C2×C3×C5×C8—21no—
50C2×C3×C5×C8—21no—
51C3×C5×C22⋊C4—21no—
52C3×C5×C22⋊C4—21no—
53C3×C42×C5C2311yescharacteristic
54C3×C22⋊Dic5—21no—
55C3×C22⋊Dic5—21no—
56C3×#685—21no—
57C3×#685—21no—
58C3×#685—21no—
59C3×#685—21no—
60C3×C4×Dic5C2×C411yescharacteristic
61C3×C4×Dic5D411yescharacteristic
62C3×C4×Dic5D411yescharacteristic
63C2×C3×#168—21no—
64C2×C3×#168—21no—
65C3×#676—24no—
66C2×C3×#124—51no—
67C3×#432—51no—
68C3×C4×M16—51no—
69C3×#329—51no—
70C3×#329—51no—
71C3×#329—51no—
72C3×#329D511yescharacteristic, complemented
73C2×Q8×D5C3×C411yescharacteristic
74C2×D4×D5C3×C411yescharacteristic
75C5×#124C22×C311yescharacteristic
76#4093C3×C411yescharacteristic
77#4082C3×C411yescharacteristic
78C2×#676—21no—
79#4031—21no—
80#4031—21no—
81D5×C22⋊C4—21no—
82D5×C22⋊C4—21no—
83#4021C22×C311yescharacteristic
84C42×D5C22×C311yescharacteristic
85C5×#97C22×C311yescharacteristic, complemented
86C5×#97C22×C311yescharacteristic, complemented
87#3952—21no—
88#3946—21no—
89C8×Dic5—21no—
90#3935C22×C311yescharacteristic, complemented
91#3935C22×C311yescharacteristic, complemented
92#1527—51noSylow
93C23×C3×C5—21no—
94C22×C3×D5—21no—
95C22×C3×D5—42no—
96C22×C3×D5—42no—
97C22×C3×D5—42no—
98C22×C3×D5C22⋊C411yescharacteristic
99C3×C5×Q8—41no—
100C3×C5×D4—41no—
101C2×C3×C4×C5—21no—
102C2×C3×C4×C5C22×C411yescharacteristic
103C2×C3×C4×C5C2×D411yescharacteristic
104C2×C3×C4×C5C2×D411yescharacteristic
105C3×C22⋊D5—42no—
106C2×C3×Dic5—21no—
107C2×C3×Dic5C22⋊C411yescharacteristic
108C2×C3×Dic5C22⋊C411yescharacteristic
109C2×C3×Dic5C22⋊C411yescharacteristic
110C3×D20—41no—
111C3×C4×D5—22no—
112C3×C4×D5—22no—
113C3×C4×D5—41no—
114C3×C4×D5—42no—
115C3×Dic10—42no—
116C3×Dic10—41no—
117C3×C5×C8—22no—
118C3×C5×C8—41no—
119C3×#168—22no—
120C3×#168—41no—
121C22×C3×Q8—51no—
122C22×C3×D4—51no—
123C2×C3×M16—101no—
124C3×#124—51no—
125C3×#124—51no—
126C3×#124—51no—
127C3×#124—101no—
128C3×#124—101no—
129C3×#124C2×D511yescharacteristic
130C2×C3×C22⋊C4—101no—
131C2×C3×C22⋊C4—101no—
132C2×C3×C42—51no—
133C3×C4⋊C8—101no—
134C3×C22⋊C8—101no—
135C3×#97—51no—
136C3×#97—51no—
137C3×#97C2×D511yescharacteristic, complemented
138C3×#97C2×D511yescharacteristic, complemented
139C3×C4×C8—101no—
140C23×D5—21no—
141C2×C5×Q8C2×C3×C411yescharacteristic
142C2×C5×D4C2×C3×C411yescharacteristic
143C2×C22⋊D5—21no—
144Q8×D5—42no—
145D4×D5—42no—
146C2×D20C2×C3×C411yescharacteristic
147C2×C4×D5—21no—
148C2×C4×D5C2×C3×C411yescharacteristic
149C2×C4×D5C3×D411yescharacteristic
150C2×C4×D5C3×D411yescharacteristic
151C2×Dic10—21no—
152C2×Dic10C2×C3×C411yescharacteristic
153C2×C5×C8—21no—
154C2×C5×C8—21no—
155C5×C22⋊C4—21no—
156C5×C22⋊C4—21no—
157C42×C5C23×C311yescharacteristic
158C22⋊Dic5—21no—
159C22⋊Dic5—21no—
160#685—21no—
161#685—21no—
162#685—21no—
163#685—21no—
164C4×Dic5C2×C3×C411yescharacteristic
165C4×Dic5C3×D411yescharacteristic
166C4×Dic5C3×D411yescharacteristic
167C2×#168—21no—
168C2×#168—21no—
169#676—24no—
170C2×#124—51no—
171#432—51no—
172C4×M16—51no—
173#329—51no—
174#329—51no—
175#329—51no—
176#329C3×D511yescharacteristic, complemented
177C22×C3×C5—41no—
178C22×C3×C5—41no—
179C22×C3×C5—41no—
180C22×C3×C5C2×C22⋊C411yescharacteristic
181C2×C3×D5—21no—
182C2×C3×D5—21no—
183C2×C3×D5—41no—
184C2×C3×D5—41no—
185C2×C3×D5—41no—
186C2×C3×D5—84no—
187C2×C3×D5#10412yes—
188C3×C4×C5—21no—
189C3×C4×C5—21no—
190C3×C4×C5—21no—
191C3×C4×C5—41no—
192C3×Dic5—21no—
193C3×Dic5—21no—
194C3×Dic5—41no—
195C3×Dic5#10012yes—
196C24×C3—101no—
197C2×C3×Q8—51no—
198C2×C3×Q8—101no—
199C2×C3×Q8—202no—
200C2×C3×Q8C4×D511yescharacteristic
201C2×C3×D4—51no—
202C2×C3×D4—101no—
203C2×C3×D4—202no—
204C2×C3×D4C4×D511yescharacteristic
205C22×C3×C4—51no—
206C22×C3×C4—51no—
207C22×C3×C4—51no—
208C22×C3×C4—101no—
209C3×M16—104no—
210C2×C3×C8—21no—
211C2×C3×C8—21no—
212C2×C3×C8—101no—
213C2×C3×C8—101no—
214C3×C22⋊C4—21no—
215C3×C22⋊C4—21no—
216C3×C22⋊C4—101no—
217C3×C22⋊C4—101no—
218C3×C22⋊C4—101no—
219C3×C22⋊C4—101no—
220C3×C22⋊C4—101no—
221C3×C22⋊C4—101no—
222C3×C42—51no—
223C3×C42—51no—
224C3×C42—51no—
225C3×C42C22×D511yescharacteristic
226C23×C5—21no—
227C22×D5—21no—
228C22×D5—42no—
229C22×D5—42no—
230C22×D5—42no—
231C22×D5C3×C22⋊C411yescharacteristic
232C5×Q8—41no—
233C5×D4—41no—
234C2×C4×C5—21no—
235C2×C4×C5C22×C3×C411yescharacteristic
236C2×C4×C5C2×C3×D411yescharacteristic
237C2×C4×C5C2×C3×D411yescharacteristic
238C22⋊D5—42no—
239C2×Dic5—21no—
240C2×Dic5C3×C22⋊C411yescharacteristic
241C2×Dic5C3×C22⋊C411yescharacteristic
242C2×Dic5C3×C22⋊C411yescharacteristic
243D20—41no—
244C4×D5—22no—
245C4×D5—22no—
246C4×D5—41no—
247C4×D5—42no—
248Dic10—42no—
249Dic10—41no—
250C5×C8—22no—
251C5×C8—41no—
252#168—22no—
253#168—41no—
254C22×Q8—51no—
255C22×D4—51no—
256C2×M16—101no—
257#124—51no—
258#124—51no—
259#124—51no—
260#124—101no—
261#124—101no—
262#124C2×C3×D511yescharacteristic
263C2×C22⋊C4—101no—
264C2×C22⋊C4—101no—
265C2×C42—51no—
266C4⋊C8—101no—
267C22⋊C8—101no—
268#97—51no—
269#97—51no—
270#97C2×C3×D511yescharacteristic, complemented
271#97C2×C3×D511yescharacteristic, complemented
272C4×C8—101no—
273C2×C3×C5—81no—
274C2×C3×C5C2×#10011yescharacteristic
275C2×C3×C5C2×#10411yescharacteristic
276C2×C3×C5#42111yescharacteristic
277C3×D5—22no—
278C3×D5—81no—
279C23×C3—21no—
280C23×C3—51no—
281C23×C3—101no—
282C23×C3—202no—
283C23×C3—202no—
284C23×C3—202no—
285C3×Q8—41no—
286C3×Q8—201no—
287C3×Q8—202no—
288C3×D4—41no—
289C3×D4—201no—
290C3×D4—202no—
291C2×C3×C4—21no—
292C2×C3×C4—51no—
293C2×C3×C4—51no—
294C2×C3×C4—51no—
295C2×C3×C4—102no—
296C2×C3×C4—102no—
297C2×C3×C4—101no—
298C2×C3×C4—201no—
299C2×C3×C4—202no—
300C2×C3×C4C2×C4×D511yescharacteristic
301C2×C3×C4D4×D511yescharacteristic
302C2×C3×C4D4×D511yescharacteristic
303C3×C8—22no—
304C3×C8—41no—
305C3×C8—102no—
306C3×C8—201no—
307C22×C5—41no—
308C22×C5—41no—
309C22×C5—41no—
310C22×C5C2×C3×C22⋊C411yescharacteristic
311C2×D5—21no—
312C2×D5—21no—
313C2×D5—41no—
314C2×D5—41no—
315C2×D5—41no—
316C2×D5—84no—
317C2×D5C3×#10412yes—
318C4×C5—21no—
319C4×C5—21no—
320C4×C5—21no—
321C4×C5—41no—
322Dic5—21no—
323Dic5—21no—
324Dic5—41no—
325Dic5C3×#10012yes—
326C24—101no—
327C2×Q8—51no—
328C2×Q8—101no—
329C2×Q8—202no—
330C2×Q8C3×C4×D511yescharacteristic
331C2×D4—51no—
332C2×D4—101no—
333C2×D4—202no—
334C2×D4C3×C4×D511yescharacteristic
335C22×C4—51no—
336C22×C4—51no—
337C22×C4—51no—
338C22×C4—101no—
339M16—104no—
340C2×C8—21no—
341C2×C8—21no—
342C2×C8—101no—
343C2×C8—101no—
344C22⋊C4—21no—
345C22⋊C4—21no—
346C22⋊C4—101no—
347C22⋊C4—101no—
348C22⋊C4—101no—
349C22⋊C4—101no—
350C22⋊C4—101no—
351C22⋊C4—101no—
352C42—51no—
353C42—51no—
354C42—51no—
355C42C22×C3×D511yescharacteristic
356C3×C5#152711yescharacteristic, complemented, Hall
357C22×C3—41no—
358C22×C3—41no—
359C22×C3—41no—
360C22×C3—52no—
361C22×C3—101no—
362C22×C3—101no—
363C22×C3—201no—
364C22×C3—201no—
365C22×C3—201no—
366C22×C3—404no—
367C22×C3D5×C22⋊C411yescharacteristic
368C3×C4—21no—
369C3×C4—21no—
370C3×C4—21no—
371C3×C4—41no—
372C3×C4—52no—
373C3×C4—101no—
374C3×C4—101no—
375C3×C4—201no—
376C2×C5—81no—
377C2×C5C2×C3×#10011yescharacteristic
378C2×C5C2×C3×#10411yescharacteristic
379C2×C5C3×#42111yescharacteristic
380D5—22no—
381D5—81no—
382C23—21no—
383C23—51no—
384C23—101no—
385C23—202no—
386C23—202no—
387C23—202no—
388Q8—41no—
389Q8—201no—
390Q8—202no—
391D4—41no—
392D4—201no—
393D4—202no—
394C2×C4—21no—
395C2×C4—51no—
396C2×C4—51no—
397C2×C4—51no—
398C2×C4—102no—
399C2×C4—102no—
400C2×C4—101no—
401C2×C4—201no—
402C2×C4—202no—
403C2×C4C2×C3×C4×D511yescharacteristic
404C2×C4C3×D4×D511yescharacteristic
405C2×C4C3×D4×D511yescharacteristic
406C8—22no—
407C8—41no—
408C8—102no—
409C8—201no—
410C2×C3—81no—
411C2×C3—102no—
412C2×C3—401no—
413C2×C3D5×#10011yescharacteristic
414C2×C3D5×#10411yescharacteristic
415C2×C3#6511011yescharacteristic
416C5C3×#152711yescharacteristic, complemented, Sylow
417C22—41no—
418C22—41no—
419C22—41no—
420C22—52no—
421C22—101no—
422C22—101no—
423C22—201no—
424C22—201no—
425C22—201no—
426C22—404no—
427C22C3×D5×C22⋊C411yescharacteristic
428C4—21no—
429C4—21no—
430C4—21no—
431C4—41no—
432C4—52no—
433C4—101no—
434C4—101no—
435C4—201no—
436C3#1059913611yescharacteristic, direct product factor, Sylow
437C2—81no—
438C2—102no—
439C2—401no—
440C2C3×D5×#10011yescharacteristic
441C2C3×D5×#10411yescharacteristic
442C2C3×#6511011yescharacteristic
subgroupG/H
centerC22×C3D5×C22⋊C4
commutatorC2×C4×C5C22×C3×C4
FrattiniC42C22×C3×D5
FittingC3×C5×#329C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×C3×D4×D5C4
cosocleC42×C5C23×C3
hypercenterC3×#329D5
hypocenterC5C3×#1527
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#329

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C3×#64996C2semidirect
3. C3×#64994C2semidirect
4. C3×C5×#329C2semidirect
5. C3×#64760C2semidirect
6. C3×#64684C2semidirect
7. C3×#64684C2semidirect
8. #10599136C3direct (N × H)
21. C3×C5×#97C22semidirect
22. C3×C5×#97C22semidirect
26. C3×#3935C22semidirect
27. C3×#3935C22semidirect
30. #64996C2×C3semidirect
31. #64994C2×C3semidirect
32. C5×#329C2×C3semidirect
33. #64760C2×C3semidirect
34. #64684C2×C3semidirect
35. #64684C2×C3semidirect
72. C3×#329D5semidirect
85. C5×#97C22×C3semidirect
86. C5×#97C22×C3semidirect
90. #3935C22×C3semidirect
91. #3935C22×C3semidirect
137. C3×#97C2×D5semidirect
138. C3×#97C2×D5semidirect
176. #329C3×D5semidirect
270. #97C2×C3×D5semidirect
271. #97C2×C3×D5semidirect
356. C3×C5#1527semidirect
416. C5C3×#1527semidirect
436. C3#10599136direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C3×D5×#1242
C3×#649962
C3×#649942
C3×C5×#3292
C3×#647602
C3×#646842
#105991363
C3×#15275